Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$

Abstract

We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$. These recursion relations allow to get explicit expressions for the Bethe vectors. Using an antimorphism of the super-Yangian $Y(\mathfrak{gl}(m|n))$, we also construct a super-trace formula for dual Bethe vectors, and, for $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$ super-Yangians, show recursion relations for them. Again, the latter allow us to get explicit expressions for dual Bethe vectors.

30 pages; typos on signs corrected

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• On Scalar Products in Higher Rank Quantum Separation of Variables
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• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains